Introduction To Finite Element Analysis And Design
2nd Edition
ISBN: 9781119078722
Author: Kim, Nam H., Sankar, Bhavani V., KUMAR, Ashok V., Author.
Publisher: John Wiley & Sons,
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For a uniformly loaded span of a cantilever beam attached to a wall at x = 0 with the free
end at x = L, the formula for the vertical displacement from y = 0 under the loaded
condition with y the coordinate in the direction opposite that of the load can be written
as follows:
Y= -(X4 – 4X³ + 6X²)
where Y is the vertical displacement, X = x/L, and L is the length of the beam.
The formula was put into dimensionless form to answer the following question: What is
the shape of the deflection curve when the beam is in its loaded condition and how does
it compare with its unloaded perfectly horizontal orientation? The answer is provided
graphically in Figure Q4.
Figure Q4 shows the vertical deflection of a uniformly loaded cantilever beam and its
comparison with the unloaded perfectly horizontal orientation.
Write a script to get the same figure as Figure Q4 by solving the following question.
1
· Unloaded cantilever beam
0.5
Uniformly loaded beam
-0.5
-1E
> -1.5
-2-
-2.5
-3
-3.5
0.5
1
1.5…
Consider the following values in the given beam above:
L1=6m
L2 = 2 m
L3 = 4 m
L4=3m
L5=2 m
L6=1m
W1 = 90 kN/m
W2 = 30 kN/m
P = 50 kN
M = 60 kN-m
Point E is an internal hinge
W1
B
L2
L3
2 m
E
W2
L5
L6
H
Classwork Problem 2
Draw the Shear Force Diagram (SFD) and
Bending Moment Diagram (BMD) for a loaded
simply supported beam shown below
1KN
5kN
2kN
4KN
1m
1m
2m
1m
1m
14
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Determine the support responses at point A of the cantilever beam shown in the figure below.arrow_forwardA simply supported beam of a total length l is shown in Figure Q5, where point A is supported by a pin connection and point C is supported by a roller support. The concentrated load is P at the location of 21/3. Determine the shear-force and bending-moment distributions produced in the beam by the concentrated load P. Note that adatpive marking has been used to consider the method mark. P 21 3 – x A C • y В Figure Q5: A simply supported beam with a concentrated load applied a) (1) The support reaction forces at the A and C, be careful of the sign.arrow_forwardA propped cantilever beam is loaded by a bending moment of the magnitude M_B at the point B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the hight ℎ that are constant along the length of the beam L. The beam material’s Young’s modulus is Q. Assuming the positive deflections and positive vertical reaction forces are upward, calculate the value of the reaction forces at points A and B the absolute value of the reaction bending moment at point A A) Let R represent the reaction force at Support B. By releasing the beam at Support B and imposing a force R at Point B, the deflection of the beam consists of two parts,i.e. Part I- the deflection caused by M_B ; Part II- the deflection caused by R Please treat R, w, h , L , E as variables in this step , the mathematical equation for the deflection at Point B caused by R ( Part II) can be written as: b) Using the provided data: cross-section width w = 14 mm, cross-section hight h = 82…arrow_forward
- A propped cantilever beam is loaded by a bending moment of the magnitude M_B at the point B as shown in Figure Q1. The cross-section of the beam is a rectangle of the width w and the hight ℎ that are constant along the length of the beam L. The beam material’s Young’s modulus is Q. Assuming the positive deflections and positive vertical reaction forces are upward, calculate the value of the reaction forces at points A and B the absolute value of the reaction bending moment at point A A) Let R represent the reaction force at Support B. By releasing the beam at Support B and imposing a force R at Point B, the deflection of the beam consists of two parts,i.e. Part I- the deflection caused by M_B ; Part II- the deflection caused by R Please treat R, w, h , L , E as variables in this step , the mathematical equation for the deflection at Point B caused by R ( Part II) can be written as: b) Using the provided data: cross-section width w = 14 mm, cross-section hight h = 82…arrow_forwardThe dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C. What is the reaction force at A? Let a positive reaction force be to the right.arrow_forwardSolve only the Galerkin Methodarrow_forward
- Given l= 1000 mm and P= 4000 N, draw internal shear force and moment diagram.arrow_forwardCantilever beam is loaded by three concentrated forces. F, 1 Given: 11= 1Ocm; 1 2 = 25cm; 1 3 = 19cm; F1 = -0.2kN; F , = -0.6kN; F 3 = -1.6kN . Find: algebraical value of reactive moment (in N m) applied at fixed point (considering counterclockwise direction as positive and clockwise as negative). Answer:arrow_forwardNote: The solution should not be hand written.arrow_forward
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